A photodetector of this type amplifies an output of a photodiode by an operational amplifier, and FIG. 4 is a circuit diagram showing an example of a configuration of a conventional photodetector A. The photodetector A comprises an operational amplifier 1, a photodiode 2 connected to an inverting input terminal of the operational amplifier 1, a plurality of (n pieces of) feedback resistors RS1 to RSn which are connected to each input terminal of an analog switch 3 at each one end and commonly connected to the inverting input terminal of the operational amplifier 1 at each other end, and the analog switch 3 for selectively connecting one ends of the feedback resistors RS1 to RSn to an output terminal of the operational amplifier 1. Such a photodetector is a kind of a feedback amplifier for providing an output voltage Vout of the operational amplifier 1 by either of a resistance value Ri of the feedback resistors RS1 to RSn which are selected by a generation current Ip of the photodiode 2 and the analog switch 3.
The magnitude relation as shown in the following equation (1) is set between respective resistance values R1 to Rn of the feed back resistors RS1 to RSn.Rn>Rn−1> . . . Ri>Ri−1> . . . >R1  (1)
The relation as shown in the following equation (2) is set so as to secure continuity of a measurement range between the respective resistance values R1 to Rn the feedback resistors RS1 to RSn. That is, the respective feedback resistors RS1 to RSn are set in the manner that the ratio between resistance values of resistors which are adjacent each other in magnitude relation between the resistance values R1 to Rn becomes ten times as large as therebetween.Ri/Ri−1=1−10  (2)
The n pieces of feedback resistors RS1 to RSn having the resistance values R1 to Rn and the analog switch 3 are provided to set a measurement range corresponding to intensity of light detected by the photodiode 2, wherein the feedback resistors RS1 to RSn are sequentially selected by the analog switch 3 to set the measurement range.
Further, the output voltage Vout of the operational amplifier 1 is given by the following equation (3) based on the generation current Ip, the resistance values R1 to Rn of the feedback resistors RS1 to RSn and an ON resistance Ron of the analog switch 3Vout=−(Ri+Ron)×Ip  (3)
The generation current Ip, i.e. intensity of light received by the photodiode 2 is obtained by measuring the output voltage Vout. The ON resistance Ron is in the order of several tens to several hundreds ohms which are smaller than the resistance values R1 to Rn of the feedback resistors RS1 to RSn but sharply varied depending on an ambient temperature, and hence it becomes the cause of an error when obtaining the generation current Ip based on the output voltage Vout.
A photodetector B shown in FIG. 5 eliminates effect by the ON resistance Ron, and has a second analog switch 4 for selecting the other ends of the feedback resistors RS1 to RSn to externally output as the output voltage Vout. Since the output voltage Vout is taken out between the feedback resistors RS1 to RSn and the analog switch 3 according to such a photodetector B, it is provided irrespective of the ON resistance Ron of the analog switch 3. Accordingly, the error caused by the ON resistance Ron is solved by such a photodetector B.
Meanwhile, although a time interval when obtaining a measurement value is designated as a sampling interval, as the sampling interval is shorter, the measurement value can be obtained in a short period of time. The sampling interval of the conventional photodetectors is determined by time needed for switching the feedback resistors RS1 to RSn by the analog switch 3. Accordingly, a type which can switch over the feedback resistors RS1 to RSn at high speed is selected as the analog switch 3, but there occurs a problem that the sampling interval cannot be shortened more because it takes time for charging and discharging electric charge caused by capacitance at an input terminal or output terminal of the analog switch 3.
FIG. 6 shows an equivalent circuit of the analog switch 3. Depicted by C1 is a capacitance between an input terminal and an output terminal of the analog switch 3, C2 is a capacitance at the input terminal thereof, and C3 is a capacitance at the output terminal thereof. The capacitances C2 and C3 are about several tens pF, and the capacitance C1 is about 0. several to several pF.
FIG. 7 shows the change of the output voltage Vout on a time basis when the feedback resistor RSi is switched to the feedback resistor Rsi−1 at a switching time T0.
Supposing that the output voltage Vout is V1 and the generation current Ip is constant when the feedback resistor Rsi is selected, the output voltage Vout on and after the switch time T0 is given by the following equation (4).Vout=Ri−1/Ri×V1=V2  (4)
Supposing that the output voltage Vout given by the equation (4) is a voltage V2, the voltage V2 is expressed by the following equation (5) based on the equation (2).V2=1/10×V1  (5)
Meanwhile, the analog switch 3 has the capacitance C1 between the input and output terminals thereof as set forth above. According to the photodetector A shown in FIG. 4, since then pieces of input terminals of the analog switch 3 are connected respectively to the inverting input terminal of the operational amplifier 1 through the feedback resistors RS1 to RSn, the feedback resistor RSi is considered to be in a state where the capacitance Cf (equivalent capacitance) each having several pF are equivalently connected in parallel with each other by the capacitance C1. Accordingly, the change of the output voltage Vout on a time basis when the feedback resistor RSi is switched to the feedback resistor RSi−1 has relaxation characteristics as shown by the line A in FIG. 7.
A time constant τ a of the relaxation characteristics is given by the following equation (6).τa=Ri−1×Cf  (6)
Further, at this time, although the voltage V1 is applied to the capacitance C2 at the input terminal of the analog switch 3 connected to the feedback resistor RSi before the switching time TO, the electric charge charged in the capacitance C2 is discharged after the analog switch 3 selected the feedback resistor RSi-1 at the switching time T0. The discharge current Id is given by the following equation (7).Id=V1/Ri×exp(−t/τb)  (7)
The time constant τb in this equation (7) is given by the following equation (8).τb=Ri×C2  (8)
The discharge current Id flows to the feedback resistor RSi−1 after the switching time T0, and appears as a voltage Vd at the time of change of the output voltage Vout. The voltage Vd is expressed by the following equation (9).Vd=Ri−1/Ri×V1×exp(−t/τb)  (9)
The voltage Vd based on the discharge current Id is to be changed as shown in dotted line B in FIG. 7.
That is, the output voltage Vout has variation characteristics as shown by a line C in FIG. 7 as a characteristic combined by the line A and the dotted line B in FIG. 7.
FIG. 8 is a view showing change of an error on a time basis after the switching time T0. An error is an absolute value obtained by dividing the output voltage Vout by the voltage V2. In the case of the output voltage Vout not considering the discharge current Id shown in the line A, it becomes the change of the error on a time bases shown in the line A in FIG. 8, and time (convergent time) required for the error to reach 0.01 is TA. Whereupon, in the case of the output voltage Vout considering the discharge current Id shown in the line C in FIG. 7, it becomes the change of the error on a time basis shown in the line B in FIG. 8, and convergent time needing to become an error equivalent to the dotted line A becomes Tb which is more longer than the convergent time Ta.
For example, supposing that Ri=10 MΩ, Ri−1=1 MΩ, Cf=2 pF, C2=10 pF, the equations τa=2 μsec, TA=10μsec, τb=100 μsec, TB=450 μsec are established. Even in the case where the feedback resistor RSi−2 is switched to the feedback resistor RSi−1, the discharge current passing through the feedback resistor RSi−2 flows but the resistance value Ri−2 of the feedback resistor RSi−2 becomes 100K Ω based on the equation of (2), and hence the time constant τb at this time becomes 1 μsec (=100KΩ×10 pF) using the above mentioned constant, which is shorter than the time constant τa, and it does not cause any problem.
In the case where the feedback resistors RS1 to RSn are switched from high resistance value to low resistance value, the discharge current passes through a high resistor, and hence a relaxation time becomes very long. Accordingly, the sampling interval cannot be shortened, and hence it is difficult to continuously measure the intensity of light ranging from high intensity to low intensity at high speed.